handbook and examples- simulation of electric and magnetic fields using femm4.20
DESCRIPTION
FEMM 4.2 ExamplesTRANSCRIPT
-
Simulation of electric and
magnetic fields using
FEMM 4.2
- User handbook and
Definition of examples
Bachelor of Science Course
In Electrical Engineering
Bachelor of Science Thesis
By Meng Weifang(992114)
Jlich, June 2011
-
This Bachelor thesis has been carried out at
Fachbereich Energietechnik
Aachen University of Applied Sciences
Jlich , Germany
This thesis was supervised by : Prof. Dr. Alexander Kern
Prof. Dr. Christoph Helsper
I certify that this work has been carried out and written up entirely by myself.
No literature references and resources other than cited have been used.
Jlich , Germany , June 2011
-
Acknowledgments
I would like to express my deepest gratitude to Prof. Dr. Alexander Kern, for
his expertise, understanding and guidance, thanks for correcting this thesis
over and over again.
And I also want to thank Prof. Dr. Christoph Helsper for his suggestions and
supervision of my project. Also I would like to thank both of my professors,
for their great help in the past several years.
At the same time, I would like to thank all Professors of FH Aachen who had
given me so much advises and help during my study in Germany.
And I would like to thank my family and my friends for their deep love and
support.
Thanks very much.
-
Contents
1. Introduction........................................................................ 8
2. Electrostatics .................................................................... 10
1.1 Cable 1 ......................................................................... 10
1.1.1 Create a new file. ........................................................................ 10
1.1.2 Set problem definition. ............................................................... 10
1.1.3 Create a model ............................................................................ 11
1.1.4 Add materials to the model ......................................................... 12
1.1.5 Define conductor properties ....................................................... 13
1.1.6 Place block labels and associate them with corresponding Materials
14
1.1.7 Generate mesh and run FEA ....................................................... 15
1.1.8 Display results ............................................................................ 15
1.1.9 Plot field values .......................................................................... 15
1.1.10 Compare with theoretical values ................................................ 18
1.2 Cable 2 ......................................................................... 18
1.2.1 Create a new file. ........................................................................ 18
1.2.2 Set problem definition. ............................................................... 19
1.2.3 Create a new model .................................................................... 19
1.2.4 Add materials to the model ......................................................... 20
1.2.5 Define conductor and material properties .................................. 20
1.2.6 Define conductor and material properties .................................. 23
1.2.7 Generate mesh and run FEA ....................................................... 23
1.2.8 Display results ............................................................................ 24
1.2.9 Plot field values .......................................................................... 24
1.2.10 Compare with the theoretical values .......................................... 25
1.3 Capacitor- Plate .......................................................... 26
1.3.1 Create a new file. ........................................................................ 26
1.3.2 Set problem definition ................................................................ 26
1.3.3 Create a new model .................................................................... 27
1.3.4 Define conductor and material properties .................................. 27
1.3.5 Set up the properties of materials and conductors ...................... 29
1.3.6 Place block labels and associate them with corresponding materials
30
1.3.7 Notice ......................................................................................... 30
1.3.8 Generate mesh and run analysis ................................................. 30
1.3.9 Plot field values .......................................................................... 31
1.3.10 Compare with theoretical values ................................................ 32
1.4 Capacitor- Cylinder ................................................... 32
-
1.4.1 Create a new file. ........................................................................ 33
1.4.2 Set problem definition ................................................................ 33
1.4.3 Create a new model .................................................................... 33
1.4.4 Define conductor and material properties .................................. 34
1.4.5 Place block labels and associate with corresponding materials . 35
1.4.6 Generate mesh and run analysis. ................................................ 36
1.4.7 Display results ............................................................................ 36
1.4.8 Plot field values .......................................................................... 36
1.4.9 Compare with theoretical values ................................................ 37
1.5 Hollow sphere 1 .......................................................... 38
1.5.1 Create a new file. ........................................................................ 38
1.5.2 Set problem definition. ............................................................... 39
1.5.3 Create a new model .................................................................... 39
1.5.4 Define conductor properties ....................................................... 40
1.5.5 Add materials to the model ......................................................... 40
1.5.6 Define conductor properties ....................................................... 41
1.5.7 Place block labels and associate them with materials. ............... 41
1.5.8 Generate mesh and run FEA ....................................................... 41
1.5.9 Display results ............................................................................ 42
1.5.10 Plot field values .......................................................................... 42
1.5.11 Comparison with the theoretical values...................................... 43
1.6 Hollow sphere 2 .......................................................... 45
1.6.1 Create a new file. ........................................................................ 45
1.6.2 Set problem definition. ............................................................... 45
1.6.3 Create a new model .................................................................... 45
1.6.4 Set the properties of materials, conductors ................................. 46
1.6.5 Place block labels and associate them with corresponding materials
47
1.6.6 Generate mesh and run analysis ................................................. 47
1.6.7 Display results ............................................................................ 48
1.6.8 Plot field values .......................................................................... 49
1.6.9 Comparison with the theoretical values...................................... 50
1.7 Plate capacitor ............................................................ 50
1.7.1 Create a new file. ........................................................................ 50
1.7.2 Set problem definition. ............................................................... 50
1.7.3 Create a new model .................................................................... 51
1.7.4 Add materials to the model ......................................................... 51
1.7.5 Define conductor properties ....................................................... 51
1.7.6 Place block labels and associate them with corresponding materials
52
1.7.7 Generate mesh and run analysis ................................................. 52
1.7.8 Display results ............................................................................ 53
1.7.9 Plot field values .......................................................................... 53
-
1.7.10 Compare with theoretical value .................................................. 54
2. Electrical Field ................................................................. 55
2.1 Cable 1 ......................................................................... 55
2.1.1 Create a new file. ........................................................................ 55
2.1.2 Set problem definition. ............................................................... 55
2.1.3 Create a new model .................................................................... 56
2.1.4 Add materials to the model ......................................................... 56
2.1.5 Define conductor properties ....................................................... 57
2.1.6 Place block labels and associate them with corresponding materials
58
2.1.7 Generate mesh and run FEA ....................................................... 58
2.1.8 Display results ............................................................................ 58
2.1.9 Plot field values .......................................................................... 59
2.2 Cable2 .......................................................................... 60
2.2.1 Create a new file. ........................................................................ 60
2.2.2 Set problem definition. ............................................................... 60
2.2.3 Create a new model .................................................................... 60
2.2.4 Define conductor properties ....................................................... 61
2.2.5 Add materials to the model ......................................................... 62
2.2.6 Place block labels and associate them with corresponding materials
63
2.2.7 Generate mesh and run analysis. ................................................ 64
2.2.8 Display results ............................................................................ 64
2.2.9 Plot field values .......................................................................... 65
3. Magnetics .......................................................................... 66
3.1 No air gap .................................................................... 66
3.1.1 Create a new file ......................................................................... 66
3.1.2 Set Problem Definition ............................................................... 66
3.1.3 Draw boundary ........................................................................... 67
3.1.4 Create a new coil ........................................................................ 67
3.1.5 Add material properties .............................................................. 68
3.1.6 Define boundary ......................................................................... 68
3.1.7 Define circuits............................................................................. 69
3.1.8 Place Block Labels ..................................................................... 69
3.1.9 Associate Properties with Block Labels ..................................... 69
3.1.10 Associate Properties with boundaries. ........................................ 71
3.1.11 Generate Mesh and Run FEA ..................................................... 71
3.1.12 Analysis result ............................................................................ 72
3.1.13 Plot Field Values ........................................................................ 74
3.2 Air gap ..................................................................................... 75
-
3.2.1 Create new file ............................................................................ 75
3.2.2 Set Problem Definition ............................................................... 75
3.2.3 Draw boundary ........................................................................... 76
3.2.4 Create a new core and coil .......................................................... 76
3.2.5 Add material properties .............................................................. 76
3.2.6 Define boundary ......................................................................... 76
3.2.7 Define circuits............................................................................. 76
3.2.8 Place Block Labels ..................................................................... 77
3.2.9 Associate Properties with Block Labels ..................................... 77
3.2.10 Associate Properties with boundaries. ........................................ 78
3.2.11 Generate Mesh and Run FEA ..................................................... 78
3.2.12 Analysis result ............................................................................ 79
3.2.13 Plot Field Values ........................................................................ 81
Bibliography ................................................................................................................................... 82
List of figures ................................................................................................................................. 83
List of tables ................................................................................................................................... 87
List of Equations ............................................................................................................................ 87
List of Files .................................................................................................................................... 87
-
0. Introduction
Finite Element Method Magnetics (FEMM) is a finite element package for solving
2-dimensional planar and axisymmetric problems in electrostatics, current flow, heat flow
and in low frequency magnetics. It is a very convenient program.
FEMM is divided into three parts:
Interactive shell (femm.exe). This program is a Multiple Document Interface
pre-processor and a post-processor for the various types of problems solved by FEMM. It
contains a CAD like interface for laying out the geometry of the problem to be solved and
for defining material properties and boundary conditions. Autocad DXF files can be
imported to facilitate the analysis of existing geometries. Field solutions can be displayed
in the form of contour and density plots. The program also allows the user to inspect the
field at arbitrary points, as well as evaluate a number of different integrals and plot various
quantities of interest along user-defined contours.
Triangle.exe. Triangle breaks down the solution region into a large number of triangles, a
vital part of the finite element process. This program was written by Jonathan Shewchuk
and is available from his Carnegie-Mellon University web page at
http://www.cs.cmu.edu/quake/triangle.html or from Netlib.
Solvers (fkern.exe for magnetics; belasolv for electrostatics); hsolv for heat flow
problems; and csolv for current flow problems. Each solver takes a set of data files that
describe problem and solves the relevant partial differential equations to obtain values for
the desired field throughout the solution domain.1
What I have done in my thesis is showing you how to analyze model using FEMM 4.2.
Here I assembled some lists of procedures that you can follow while solving problems
Electrostatics procedures:
1. Create a new file. Choose a type of the problem
2. Set problem definition.
3. Create a model.
4. Add materials to the model.
5. Define conductor properties.
6. Place block labels and associate them with corresponding Materials.
7. Generate mesh and run FEA.
8. Display results.
9. Plot field values.
10. Compare with theoretical values
1 Finite Element Method Magnetics: Version 4.2Users ManualDavid Meeker May 29, 2009
-
Current flow procedures:
1. Create a new file. Choose a type of the problem
2. Set problem definition.
3. Create a model.
4. Add materials to the model.
5. Define conductor properties.
6. Place block labels and associate them with corresponding Materials.
7. Generate mesh and run FEA.
8. Display results.
9. Plot field values.
10. Compare with theoretical values
Magnetics procedures:
1. Create new file.
2. Set Problem Definition.
3. Draw boundary.
4. Create a new coil
5. Add material properties.
6. Define boundary .
7. Define circuits.
8. Place Block Labels.
9. Associate Properties with Block Labels
10. Associate Properties with boundaries.
11. Generate Mesh and Run FEA.
12. Analysis result.
13. Plot Field Values .
14. Compare with theoretical values
When we have to make a new model, first of all we should decide if we want to make it in
planar of axisymmetric. Choose it wisely, because it may save you a lot of time if the model
can be made in axisymmetric type.
When we have the plotted field values, we can use them to analyze the property along a
contour. A contour is a line or region that we are interested in. Then we can compare it with
the theoretical values. If those values match, it means the model we have made is correct. If
they didnt, then we have to look deeper into the model and find out what has gone wrong.
-
1. Electrostatics
What is Electrostatics?
Electrostatics is the study of time-independent distributions of charges and fields.
It is a branch of science that deals with the phenomena arising from stationary or
slow-moving electric charges.Electrostatic phenomena arise from the forces that electric
charges exert on each other.2
Electrostatics contains some problems like properties analyzing in capacitors and in some
containers. No current is involved in Electrostatics.
1.1 Cable 1
Assume we have a perfect concentric copper cable. At inner cable a voltage of 130kV
(compare to the ground) is applied. (relative permittivity of copper r 1) Layer 1 Layer 2
r 3 2
Table 1-1 Values of the relative permittivityr
We will analyze the curve E=f(r) of this cable and draw a plot of E=f(r).
1.1.1 Create a new file.
FileNew Electrostatics Problem
Figure 1-1 Create a new problem dialogue box
1.1.2 Set problem definition.
Press Menu: Problem.
Figure 1-2 Problem definition dialogue box
2Electrostatics: Theory and Applications by Camille L. Bertrand
-
Problem Type: Axisymmetric
Length Unit: Centimeters
Frequency, Hz: 60
Depth: 1
Solver Precision: 1e-008
Min Angle: 30
1.1.3 Create a model
Draw three quarters of circle using function Operate on arc Segments. First we
should mark some nodes using Operate on nodes, then we switch to function .
Select 2 nodes one by another to draw an arc segments in between.
Figure 1-3 New model
Properties of the circles are shown in the picture. We can check this information by right
clicking on the arc segment under the function . And we can also do the same thing
under function to check the information of a drawn linear segment.
Figure 1-4 Linear property
-
1.1.4 Add materials to the model
Set up the information of material (schicht1, schicht2, inner, air) and conductor (layer1,
layer2, gnd), using the functions under menu Properties.
Figure 1-5 Properties menu
The voltage on each layer must be calculated first.
Cylinder- capacitor
Table 1-2 Formula
Figure 1-6Cylinder capacitor3
If we want to define the voltages, click on Conductors and then fill in the names and values.
Here we have the values of voltage, so we fill the blank under Prescribed Voltage.
Otherwise we can fill the Total Charge, C if we have the value in unit Column.
Voltage on Layer 1 is the total voltage (130kV) from center of cable to the ground.
3http://upload.wikimedia.org/wikipedia/commons/b/b8/Cylindrical_CapacitorII.svg
C1/C2=3/2
U1/U2=C2/C1=2/3
Uges=U1+U2=130kV
U1=52kV U2=78kV
Equation 1
-
Figure 1-7 Voltage on layer 1
Ground
Figure 1-8 Ground
Select an arc segment, press Space button and then in the column in conductor, we can
choose which conductor it should be in. As shown below.
Figure 1-9 Layer 1, 2, 3
1.1.5 Define conductor properties
The properties of material are already given, r of material in schicht1 is 3; r of material in schicht2is 2. We use PropertiesMaterials to define them.
Here we give both x and y the same number. In this way, r will be determined as the
value we need.
r =3 for schicht1
Figure 1-10Property of material 1
-
r=2 for schicht2
Figure 1-11Property of material 2
1.1.6 Place block labels and associate them with corresponding
Materials
Set the inner block as schicht1, the outer block as schicht2, using function Operate on
block labels. Left click on a closed area to mark the label, then right click on the label and
press Space button to call the menu.
Under Block type, we can mark the block as any materials that we have set before. This
means we will build this layer with this material. Uncheck Let Triangle choose Mesh Size
and make size to 0.1 so that the result is fine enough.
Figure 1-12 Properties for selected block dialogue box
Figure 1-13 Final model
-
1.1.7 Generate mesh and run FEA
Run the analysis, first press Run mesh generator, then you can see the meshes it
created. If you forgot to label a block, the area will be gray, so that you should label that area.
Figure 1-14 Mesh
1.1.8 Display results
Press Run analysis, after few seconds when its done, click the button View
Result and the result is shown here.
Figure 1-15 Result
The result is the density plot of a concentric cable.
1.1.9 Plot field values
Here we can draw any plots we need to use the function X-Y plot of field values.
Under plot type, we can select the ones we need. And we can set the number of points in plot,
so it will calculate more points if we need. In this case, we make the number 1000.
-
Figure 1-16 X-Y plot of field Values dialogue box
But before that, we need to select a contour to decide which part of the object which we are
interested in.
Switch to Contour mode by pressing the Contour Mode toolbar button. Now we can define a
contour along which the properties will be plotted. There are three methods to add points or
areas to a contour :
1. Left Mouse Button Click adds the nearest input node to the contour;
2. Right Mouse Button Click adds the current mouse pointer position to the contour;
3. Key displays a point entry dialog that allows you to enter in the coordinates of a
point to be added to the contour.
Here we need the plot along a radius. So we press and right click on (0,0) and (14.1, 14.1)
to draw two points, making up a segment as following. The contour is a vector so we have to
decide its direction as well. If we left click on the graph, then the program will automatically
choose the nearest node as the point.
Figure 1-17 Contour
Now we can draw the plot we need to analyze the properties along the contour. We need E,t
plot (tangential electrical field intensity) here.
-
Figure 1-18E,t plot
And this plot can be used to analyze the component.
If we dont change the number of points, the default value will be 150.
Figure 1-19 Change number of points in plot
This is the plot when the number is 150, which is rougher than the plot above.
Figure 1-20E,t plot with 600 points in it
-
1.1.10 Compare with theoretical values
Since we have already calculated the voltage on each layer, we can use the result plot to
check our work.
Click on menu View Point Props to view the detail information of points. Click on the point that you are interested in and you will get the detail information of it.
Figure 1-21 Point Props
As is shown here, we picked the point (0, 10), and its info is in figure 1-22
Figure 1-22 Point info
As we calculated before, the voltage on this layer should be 52kV, and here we get 55.6kV, a
little bit higher than the theoretical value. But the difference is acceptable, so it is correct.
1.2 Cable 2
Assume we have a non-concentric copper cable. The inner cable is 3mm aside from the
center. At the inner cable a voltage of 130kV (compare to the ground) is applied. (relative
permittivity of copper r 1) Layer 1 Layer 2
r 10 1
Table 1-3 Values of the relative permittivityr
We will analyze the curve of E=f(r) of this cable and draw a plot of it.
1.2.1 Create a new file.
FileNew Electrostatics Problem
-
1.2.2 Set problem definition.
Press Menu: Problem.
Figure 1-23 Problem definition dialogue box
1.2.3 Create a new model
To draw a set of non-concentric circles, first we need to have three concentric circles using
function Operate on arc Segments. First we should mark some nodes using
Operate on nodes, then we switch to function . Select 2 nodes one by another to draw
an arc segments in between, and then we will have half of the circle. Now we need the other
half so we select these 2 nodes again but this time change the selection order. In this way, we
will be able to make all three circles.
Figure 1-24 New model step 1
Our model is a non-concentric cable, so we shift the inner circle, using Move/Remote the
selected Object. First switch to function and select the inner circle. Press , shift it
along X-axis for 3 units.
-
Figure 1-25 New model step 2
1.2.4 Add materials to the model
Set up the information of material (schicht1, schicht2, center, air) and conductor (layer1,
layer2, gnd), using the functions under menu Properties.
Figure 1-26 Properties menu
But set the middle circle to In conduct: None, we regard it as a non-material layer.
Cylinder- capacitor
Table 1-4 Formula
Figure 1-27 Cylinder capacitor4
1.2.5 Define conductor and material properties
The voltage on each layer can be calculated first. If the cable is symmetric:
4http://upload.wikimedia.org/wikipedia/commons/b/b8/Cylindrical_CapacitorII.svg
-
But here we have a non-symmetric cable, so the values we calculated can only be used as
references
.
If we want to define the voltages, click on Conductors and then fill in the names and values.
Here we have the values of voltage, so we fill the blank under Prescribed Voltage.
Otherwise we can fill the Total Charge, C if we have the value in unit Colum.
Voltage on Layer 1 is the total voltage (130kV) from center of cable to the ground.
Figure 1-28 Voltage on layer 1
Ground
Figure 1-29 Ground
Select an arc segment, hit space bar and then in the column in conductor, we can choose
which conductor it should be in. As shown below.
But set the middle circle to In conduct: None, we regard it as a non-material layer.
C1/C2=10/1
U1/U2=C2/C1=1/10
Uges=U1+U2=130kV
U1=11.82kV U2=118.18kV
Equation 2
-
Figure 1-30 Layer 1 None Gnd
The properties of material are already given, r of material in schicht1 is 10; r of material
in schicht2is 1. We use PropertiesMaterials to define them.
Here we give both x and y the same number. In this way, r will be determined as the
value we need.
r = 10 for schicht1
Figure 1-31Property of material 1
r= 1 for schicht2
Figure 1-32Property of material 2
And also set the properties of center which is made by copper, whose relative permittivity
is 1. We must set all the properties of all blocks so that the program can begin analysing.
Figure 1-33Property of material 3
-
1.2.6 Define conductor and material properties
Set the center block as center, inner block as schicht1, the outer block as schicht2,
using function Operate on block labels. Left click on a closed area to mark the label,
then right click on the label and press Space button to call the menu.
Under Block type, we can mark the block as any materials that we have set before. This
means we will build a layer with this material.
And here we also uncheck the option and set the mesh size to 0.1.
Figure 1-34 Properties for selected block dialogue box
1.2.7 Generate mesh and run FEA
Run the analysis, first press Run mesh generator, then you can see the meshes it
created. If you forgot to label a block, the area will be gray, so that you should label that area.
Figure 1-35 Mesh
-
1.2.8 Display results
The density plot of a cable, which is not perfectly concentric, is shown here.
Figure 1-36 Result
Figure 1-37 Result (zoom)
From this picture we can clearly see the obvious differences between this cable and a
concentric cable like Cable 1.
1.2.9 Plot field values
The contour is a vector, so we have to decide its direction as well. Choose the contour starts
from (3, 0), ends in (20,0), as following.
-
Figure 1-38 Contour
Then select E, t plot with number of points 1000 in it.
Figure 1-39 E,t plot
1.2.10 Compare with the theoretical values
The theoretical values we calculated before were for a concentric cable.Here we have a
non-concentric cable. Although our cable is not symmetric, but the voltage differences are
caused by the distance difference between center and layers. So if we add the voltages on
two points along a diameter together, the result should be equal to the sum of the voltages on
the same two points when they are in a concentric cable.
So we have to check two points, which are (10, 0) and (-10, 0).
Figure 1-40 Voltages on two points U1 and U2
U1+ U2= 125603V+ 110798V= 236.401kV
2* U1= 236.36 kV
So the theoretical value equals the practical value. This means our model is correct.
1.8e+006
1.8e+007
-
1.3 Capacitor- Plate
Figure 1-41 Ue8-1
Inner cable 2*ri=10 mm Flange (Flansch) diameter 2*ra=100 mm
Flange length la=100 mm Ed=20 MV/m
The total voltage applied is 115 kV (compare to the ground).
If r= const. The lengths of metal pads are l1 l4. If the model is treated as a homogenous
field (Plate capacitor) with an isodynamic voltage divide.
We will draw the field profile E=(r).
1.3.1 Create a new file.
FileNew Electrostatics Problem
1.3.2 Set problem definition
Menu Problem
Figure 1-42 Problem definition dialogue box
la
ri
r
ra
-
1.3.3 Create a new model
We treat the model as a homogenous field so it should be a Plate capacitor.
1.3.4 Define conductor and material properties
First of all, we must calculate the values of Rx and Lx.
I 1 2 3 4 5
Rx 5 14 23 32 41 50
Lx / 519 250 166 125 100
Table 1-5 Calculated values of Rx and Lx
Figure 1-43 Nodes
To draw such a model, we have several methods. Here I will show you two of them.
Mark one node randomly. Select the node and press TAB, then type in the
coordinate of node.
Figure 1-44 Enter point dialogue box
Then we can see a new point is copied to the new coordinate.
Find (0, 0), use function copy
-
Figure 1-45 Copy dialogue box
Select translation horizontal shift, and give a value that we need. Repeat this procedure several times until we get all points we need. As
shown.
Figure 1-46 x-axis
Then use copy function to copy every nodes above and under x-axis. In
this way, we can set coordinates of the points precisely.
This is the model we need to solve this problem. Use function to draw all the segments
between nodes.
Figure 1-47 Final model
x-axis
-
1.3.5 Set up the properties of materials and conductors
The material is irrelevant for the voltage distribution, if it is the same in the entire lead
through, so we just add air=1.
Figure 1-48 Property of material
We set l5=la=100mm as Gnd and l1 as 115kV and then calculate the voltages on each layer
one after another.
Click on Conductors and then fill in the names and values so we can set the information of
Voltages.
Set the total voltage to 115000V. Attach every layer with its conductor. The layers in
between are set to conductor: None, and the two outer layers are set as following:
Figure 1-49 Conductor 1
Figure 1-50 Total voltage
-
Figure 1-51 Conductor 2
Figure 1-52 Ground
1.3.6 Place block labels and associate them with corresponding
materials
Set up block properties, using function Operate on block labels. Left click on a closed
area to mark the label, then right click on the label and press Space button to call the menu.
We set every block between 2 boards to air. (air: x = y= 1)
1.3.7 Notice
If the program cant calculate the mesh, which means the angle is too small to calculate,
click on to adjust the minimal angle to 1.
1.3.8 Generate mesh and run analysis
Now save the file and click on the toolbar button with yellow mesh . And the result is
shown here.
-
Figure 1-53 Result
1.3.9 Plot field values
Then choose a horizontal contour to draw the electrical field plot for this module. Select plot
type E, t.
Figure 1-54 Result (zoom)
Figure 1-55E,t plot
From the plot we can see the model is perfect homogenous. And it matches the facts.
-
1.3.10 Compare with theoretical values
Because the U=constant=23kV so voltage on each layer can be easily calculated. U1=92kV U2=69kV U3=46kV U4=23kV
Figure 1-56 Info on each layer
Practical values and theoretical values match. This means our model is correct.
1.4 Capacitor- Cylinder
Figure 1-57 Ue8-2
-
Inner cable 2*ri=10 mm Flange(Flansch) diameter 2*ra=100 mm
Flange length la=100 mm Ed=20 MV/m
The total voltage applied is 115kV(compare to the ground).
If r = const. The lengths of metal pads are l1 l4. If the model is treated as a cylinder field
with an isodynamic voltage divide.
Here we will draw the field profile E=(r).
1.4.1 Create a new file.
FileNew Electrostatics Problem
1.4.2 Set problem definition
We can use the default definitions here.
1.4.3 Create a new model
When this model is treated as a cylinder field, we draw the cross section of the cable. First
step, draw 6 concentric circles.
Calculate rx and lx first, and then mark all the points in coordinate.
Figure 1-58 Capacitor
konst
Equation 3
-
I 1 2 3 4 5
Rx 5 14 23 32 41 50
Lx / 519 250 166 125 100
Table 1-6 Calculated values for Rx and Lx
Mark some nodes using Operate on nodes, then switch to function . Select 2 nodes
one by another to draw an arc segments in between. Then select again in the other way
around. So we will get a complete circle. Finish the rest circles.
Figure 1-59Model Cross section
1.4.4 Define conductor and material properties
Cylinder- capacitor
Table 1-7 Formula
Figure 1-60Cylinder capacitor5
Figure 1-61 Material properties
5http://upload.wikimedia.org/wikipedia/commons/b/b8/Cylindrical_CapacitorII.svg
-
Figure 1-62 Conductor properties
Figure 1-63 Conductor attachments
Set the center layer to conductor 115kv and the outer layer to Gnd. Rest of the layers are
set in conductor:None.
1.4.5 Place block labels and associate with corresponding materials
Use function Operate on block labels. Left click on a closed area to mark the label, then
right click on the label and press Space button to call the menu. We set the center block to
metal because its a metal rod, and the rest blocks will be set as air.
Figure 1-64 Final model
-
1.4.6 Generate mesh and run analysis.
Mesh size is set to 1 in this case, and we can get 14000 meshes.
Figure 1-65 Mesh
1.4.7 Display results
The density plot will be looking like this.
Figure 1-66Result
1.4.8 Plot field values
Select a contour, the contour is a vector so we have to decide its direction as well. Here
we draw it from inner to the outer shell. Use the function so that we can select
nodes directly.
-
Figure 1-67Contour
Use function to draw the plot of electric field.E,t (tangential electrical field
intensity) plot is shown below.
Figure 1-68E,t plot
1.4.9 Compare with theoretical values
Because the U=constant=23kV so voltage on each layer can be easily calculated. U1=92kV U2=69kV U3=46kV U4=23kV
-
Figure 1-69 Info on each layer
Practical values and theoretical values match. This means our model is correct.
1.5 Hollow sphere 1
Now, if we are given a problem that involves a point charge, how do we solve it? A point
charge is a particle which is zero-dimensional, does not take up space. A point particle is
an appropriate representation of any object whose size, shape, and structure is irrelevant
in a given context.6
How do we represent such a particle using this program? Lets try it by two different
methods.
A positive point charge Q is centered in a metal hollow sphere. Inner radius R1, Outer radius
R2. The Sphere is connected with ground, the potential of the sphere is zero.
Here we will draw a plot of the field profile E=(r)
First of all, I should notice you that this method is not correct.
1.5.1 Create a new file.
FileNew Electrostatics Problem
6H.C. Ohanian, J.T. Markert (2007). Physics for Engineers and Scientists. 1 (3rd ed.). Norton. ISBN 9780393930030.
R1
R2
Figure 1-70 Hollow sphere
-
1.5.2 Set problem definition.
Press Menu: Problem.
Figure 1-71 Problem Definition
1.5.3 Create a new model
Then, simply draw a circle as shown
Figure 1-72 New model
Draw a node on the center of circle, and we will use it as the point charge later.
Figure 1-73 Node in center of circle
-
1.5.4 Define conductor properties
Set properties of material, conductor and point. The nodal properties must be set ahead.
Menu Properties Point Add Property
Figure 1-74 Nodal property dialogue box
In nodal property, we set the point charge density as 100C/m . In the Problem definition, we
have set the depth to 1 mm. So the point charge has 100C/m* 0.001m= 0.1C.
Sphere capacitor
Sphere Table 1-8 Formula
Figure 1-75Sphere Capacitor7
1.5.5 Add materials to the model
We set r air as 1.
Figure 1-76Material property
7http://upload.wikimedia.org/wikipedia/commons/3/3f/Spherical_Capacitor.svg
-
1.5.6 Define conductor properties
The outer shell is connected with ground, so we set it as Gnd. Select the outer shell and
press Space bar to set the further properties.
Figure 1-77Attach conductors to their properties
First, select the node in the center of circle by left clicking on it under
function Operation on node. Then press Space bar to pop the dialogue box, where we
can define the property of a node. Select Nodal Property to Q, which we have defined
already.
Figure 1-78Attach node to its property
1.5.7 Place block labels and associate them with materials.
Set the only block as air.
1.5.8 Generate mesh and run FEA
The mesh size was chosen by triangle.
Figure 1-79
-
1.5.9 Display results
Run analyses and we will get a plot as below. As we can see, the result is not in circles but in
some shapes like Hexagons, which is very strange but interesting.
Figure 1-80 Result
1.5.10 Plot field values
Draw E (electrical field intensity) and D (flux density) plot for this module.
Figure 1-81 Contour
Figure 1-82E,t plot
-
Figure 1-83D,t plot
1.5.11 Comparison with the theoretical values
If this method is correct, we should get a plot of function , but the curve
does not match the facts. This method is not available.
And there is one more interesting thing. The electrical field density is not symmetric
according to the plot. So I ran a mesh generate as well.
Figure 1-84 Mesh
As we can see, the meshes arent perfectly symmetric either.
If we uncheck the box Let the triangle choose mesh size and set it to a very small value, for
example 0.1.
-
Figure 1-85 Uncheck the box
Figure 1-86 New meshes
Run analysis again.
Figure 1-87 New result
-
And this time it seems to be smoother. But if we zoom in a little, we can still see that the
center is not a circle.
Figure 1-88 New zoom
Thus, I assume the node in this program may have a shape, and probably not a perfect
model of point.
1.6 Hollow sphere 2
Here we do the same problem once again, but in a correct way.
1.6.1 Create a new file.
FileNew Electrostatics Problem
1.6.2 Set problem definition.
Press Menu: Problem. And we can use the default definitions.
1.6.3 Create a new model
Draw a circle to make the shell of the capacitor.
Figure 1-89 New model
-
Draw a little circle on the center of it, used as the point charge.
Figure 1-90 Circle in the center
1.6.4 Set the properties of materials, conductors
Sphere capacitor
Sphere Table 1-9Formula
Figure 1-91 Sphere capacitor8
Figure 1-92 Properties of material
Figure 1-93 Properties of conductor
8http://upload.wikimedia.org/wikipedia/commons/3/3f/Spherical_Capacitor.svg
-
The outer shell is connected with ground, so we set it as Gnd. Select the outer shell and press
Space bar to set the further properties.
Figure 1-94 Attach conductor to its property (part 1)
Use the little circle as a point charge. Set its conductor as Punktladung
Set the conductor property of the little circle as Punktladung and the other block will be set
as air. The radius of this little circle is 0.1mm in this case and dont forget to select both
halves of the circle.
Figure 1-95 Attach conductor to its property (part 2)
1.6.5 Place block labels and associate them with corresponding
materials
Set the block as air. And in this case, set the mesh size of both blocks to 0.025.
1.6.6 Generate mesh and run analysis
-
Figure 1-96 Mesh
Figure 1-97 Mesh (zoom)
1.6.7 Display results
Figure 1-98 Result
-
1.6.8 Plot field values
Draw E and D plot for this module. First choose the contour . Connect the two nodes
(0, 0.1) and (0, 40).
Figure 1-99 Contour
Figure 1-100 X-Y plot of field values dialogue box
We choose E,t here because we need electrical field along the red line. Normal field means
the field vertical to the line we chose. So is D,t.
If you find your curve too rough, you can go back to 1.6.6 to change the mesh size and run
the analysis again. The smaller the mesh size is, the finer your curve may get.
Figure 1-101E,t plot
-
Figure 1-102D,t plot
1.6.9 Comparison with the theoretical values
This plot matches the facts. So this is the right method to solve the problem with point
charge.
1.7 Plate capacitor
A capacitor is made of 3 thin metal plates. The area of those plates are A=100 . The
capacitor will be first connected to a voltage supply U=1750 V and then separate from it.
Please draw a field profile E=(r)
1.7.1 Create a new file.
FileNew Electrostatics Problem
1.7.2 Set problem definition.
Press Menu: Problem.
Figure 1-103 Problem Definition
-
1.7.3 Create a new model
Draw 3 segments which parallel to x-axis. Then connect the nodes so we get a Plate
capacitor like this.
Figure 1-104 New model
1.7.4 Add materials to the model
Set properties of material and conductor
Figure 1-105 Properties of material 2
Figure 1-106 Properties of material 2
1.7.5 Define conductor properties
Plate capacitor
Table 1-10 Formula
Figure 1-107 Plate capacitor9
9http://upload.wikimedia.org/wikipedia/commons/2/20/Plate_CapacitorII.svg
-
Figure 1-108 Properties of conductor
Set the conductor information of the three segments, from top to bottom, as top and
bottom. Select each segment under function Operate on segment, press Space
bar to call the dialog box.
Figure 1-109Attach conductors to their properties
1.7.6 Place block labels and associate them with corresponding
materials
Set material of the blocks schicht1 (upper half), schicht2 (lower half). And here we can let
the triangle choose the mesh size.
1.7.7 Generate mesh and run analysis
Figure 1-110 Mesh
top
bottom
-
1.7.8 Display results
Figure 1-111Result
1.7.9 Plot field values
Draw E and D plot for this module. First draw the contour from top to bottom
as is shown in figure 1-107. Then draw the plot .
Figure 1-112Contour
Choose E,t (tangential field intensity) plot
Figure 1-113 X-Y plot of field values dialogue box
-
Figure 1-114E,t plot
1.7.10 Compare with theoretical value
Figure 1-115 Voltages
So the voltage on middle layer should be 1750V* 3/4= 1312.5V. And according to the
Points props, our model is correct.
Figure 1-116 Detail info
.
C1:C2= 1: 2= 3:1 U1/U2= C2/C1= 1/3
U1
U2
Equation 4
-
2. Electrical Field
Before we deal with some current flow problems, we should first understand--
What is an electrical field?
In physics, an electric field surrounds electrically charged particles and time-varying
magnetic fields. This electric field exerts a force on other electrically charged objects.
Michael Faraday introduced the concept of an electric field.
The electric field is a vector field with SI units of newtons per coulomb (N/ C) or,
equivalently, volts per meter (V/m). The strength or magnitude of the field at a given point is
defined as the force that would be exerted on a positive test charge of 1 coulomb placed at
that point; the direction of the field is given by the direction of that force. Electric fields
contain electrical energy with energy density proportional to the square of the field
amplitude. The electric field is to charge (E=F/q) as gravitational acceleration is to mass
(a=g*m/r2 ) and force density is to volume (f= dF/dV).
An electric field that changes with time, such as due to the motion of charged particles in the
field, influences the local magnetic field. That is, the electric and magnetic fields are not
completely separate phenomena; what one observer perceives as an electric field, another
observer in a different frame of reference perceives as a mixture of electric and magnetic
fields. For this reason, one speaks of "electromagnetism" or "electromagnetic fields". In
quantum mechanics, disturbances in the electromagnetic fields are called photons, and the
energy of photons is quantized.10
2.1 Cable 1
Assume we have a perfect concentric cable. At inner cable a voltage of 130kV (compare to
the ground) is applied.
Layer 1 Layer 2
r (S/m) 3 2 Table 2-1 Value of the electrical conductivity
We will draw the field profile E=f(r) of this cable as well as a plot of E=f(r).
2.1.1 Create a new file.
FileNew Current Flow Problem
2.1.2 Set problem definition.
Press Menu: Problem. Change problem type to Axisymmetric and Unit length to
millimeters.
10Electric field in "Electricity and Magnetism", R Nave
-
2.1.3 Create a new model
Draw three quarters of circle using function Operate on arc segment.
Figure 2-1 New model
2.1.4 Add materials to the model
Set up the properties of material (schichte1, schichte2, inner, air). The values of the
material are already given, r of material in schicht1 is 3; r of material in schicht2is 2.
Here we give both x and y the same number. In this way, r is determined.
r =3 for schicht1
Figure 2-2 Property of material 1
r=2 for schicht2
Figure 2-3 Property of material 2
-
2.1.5 Define conductor properties
Set the properties of conductors (layer1, layer2, gnd).
The voltage on each layer must be calculated first.
Electrical conductivity
Unit: S/m
Electrical resistivity
is the static resistivity (measured in ohm-meters, m) E is the magnitude of the electric field (measured in volts per meter, V/m);
J is the magnitude of the current density (measured in amperes per square meter, A/m).
Voltage on Layer 1 is the total voltage (130kV) from center of cable to the ground.
Figure 2-4 Voltage on layer 1
Ground
Figure 2-5Voltage on layer 3
Equation 5
-
2.1.6 Place block labels and associate them with corresponding
materials
Set the inner block as schicht1, the outer block as schicht2. Then change the mesh size to
0.1.
Figure 2-6 Final model
2.1.7 Generate mesh and run FEA
Figure 2-7 Mesh
2.1.8 Display results
Run the analysis, and the result is shown here
.
Figure 2-8 Result
-
Draw the contour from (0, 0) to (14.1, 14.1). The result is the density plot in a concentric
cable.
Figure 2-9 Contour
2.1.9 Plot field values
We can choose the |E| plot here, so the {Re} and {Im} part wont be shown separately.
Figure 2-10|E| plot
This is what it looks like when we choose E,t plot again.
Figure 2-11E,t plot
-
2.2 Cable2
Assume we have a non-concentric cable. The inner cable is 3mm aside from the center. At
the inner cable a voltage of 130kV (compare to the ground) is applied. (Type: AC Frequency:
50Hz DC=0V)
Layer 1 Layer 2
r (S/m) 10 1 Table 2-2 Values of the electrical conductivity
Here we will draw the field profile E=f(r) of this cable as well as a plot of E=f(r).
2.2.1 Create a new file.
FileNew Current Flow Problem
2.2.2 Set problem definition.
Press Menu: Problem. Change problem type to Planar and units to centimeters.
2.2.3 Create a new model
Draw three concentric circles with given radii. To draw a set of non-concentric circles, first
we need to have three concentric circles using function Operate on arc Segments. First
we should mark some nodes using Operate on nodes, then we switch to function .
Select 2 nodes one by another to draw an arc segments in between, and then we will have
half of the circle. Now we need the other half so we select these 2 nodes again but this time
change the selection order. In this way, we will be able to make all three circles.
Figure 2-12New model step 1
-
Figure 2-13 New model step 2
2.2.4 Define conductor properties
First we need to calculate the voltages on each shell.
Voltage on Layer 1 is the total voltage (130kV) from center of cable to the ground. Voltage
on Layer 2 is U2.The rest layer is Ground
Figure 2-14 Voltage on layer 1
Figure 2-15 Gnd
Equation 6
-
Select an arc segment, press Space button and then in the column in conductor, we
associate them with matching conductors.
Set up the properties of conductor and material. But set the middle circle to In conduct:
None, we regard it as a non-material layer. The other settings remain the same. As shown
below.
Figure 2-16 Attach conductor to its property
Figure 2-17 Layer 1 Gnd
2.2.5 Add materials to the model
The properties of material are already given,r of material in schicht1 is 10; r of material in schicht2is 1. We use PropertiesMaterials to define them. Here we give both x and y the same number. In this way, r will be determined as the value we need.
r =10 for schicht1. The relative electrical permittivity cant be 0, so we make it 1 here, but it doesnt influence the result.
Figure 2-18 Property of material 1
-
r=1 for schicht2
Figure 2-19Property of material 2
2.2.6 Place block labels and associate them with corresponding
materials
Set the inner block as schicht1, the outer block as schicht2, using function Operate on
block labels. Left click on a closed area to mark the label, then right click on the label and
press Space button to call the menu. Then we can associate them with corresponding
materials.
Set the mesh size to 0.1 in this case as well.
Figure 2-20 Final model
-
2.2.7 Generate mesh and run analysis.
Figure 2-21 Mesh
2.2.8 Display results
This is a density plot of a cable, which is not perfectly concentric, is shown here.
Figure 2-22 Result
Figure 2-23 Result (zoom)
-
2.2.9 Plot field values
Choose contour from (3,0) to (20, 0)
Figure 2-24 Contour
Draw contour from center of the inner circle to the outer shell. Then if we draw E,t plot here,
we will get a plot with Real and Imaginary part of current.
Figure 2-25E,t plot
But if we want the curve of the total current, we choose |E| (Magnitude of electrical field
intensity).
Figure 2-26 |E| plot
-
3. Magnetics
What is magnetics?
A magnetic field is a field of force produced by moving electric charges, by electric fields
that vary in time, and by the 'intrinsic' magnetic field of elementary particles associated with
the spin of the particle. There are two separate but closely related fields to which the name
'magnetic field' can refer: a magnetic B field and a magnetic H field. The magnetic field at
any given point is specified by both a direction and a magnitude (or strength); as such it is a
vector field. The magnetic field is most commonly defined in terms of the Lorentz force it
exerts on moving electric charges.11
3.1 No air gap
Assume we have a square coil built up by 50 turns of copper wire (16 AWG). The length of
its side is 6cm. And through the wire flows a 60A current.
Figure 3-1 Coil wrapped up with copper wire
We will draw the field profile of its magnetic flux density and also the B- and H-field plots.
3.1.1 Create a new file
FileNew Current Flow Problem
3.1.2 Set Problem Definition
Problem Type: Planar
Length Units: Centimeters
Frequency: 0
Depth: 1
Solver Precision
Min Angle: 30
AC Solver: Succ. Approx
11, by Rothwell and Cloud
-
Figure 3-2 Problem definition
3.1.3 Draw boundary
Draw a boundary to be the solution region that we are interested in. The shape and area of
this region can be selected as you want. Here, we draw it as a square, so that we can have an
axisymmetric solution. Point nodes at (-5, -5), (-5, 11), (11, -5), (11, 11), then connect them
to make a square boundary.
3.1.4 Create a new coil
Draw 2 squares in the center of boundary to make the core. Point nodes at (0, 0), (0, 6), (6, 0),
(6, 6). Connect the nodes to make the first square. Point nodes at (1, 1), (1, 5), (5, 1), (5, 5),
connect them to make the second.
Figure 3-3 Core
Point nodes at (-0.25, 4.5), (-0.25, 1.5), (0, 4.5), (0, 1.5), (1, 4.5), (1, 1.5), (1.25, 4.5), (1.25,
1.5). Then connect them as shown to make the coil.
.
Figure 3-4 Coil
-
3.1.5 Add material properties
PropertiesMaterials Library
Figure 3-5 Material Library
Find the material we need in this library and drag it to the Model Materials box. Here we
need copper 16 AWG, which is under Copper AWG Magnet Wire, Pure Iron under Soft
magnetic material. And also we need material Air.
3.1.6 Define boundary
Select PropertiesBoundary from the main menu , then click on the Add Property button. Rename the boundary to A=0and Select type to Prescribed A, which means here
we selected Dirichlet to be the boundary condition. Fill all the values with 0. Then click on
OK.
(There are 5 boundary conditions for magnetic problems:
Dirichlet. In this type of boundary condition, the value of potential A or V is explicitly defined on the
boundary.
Neumann. This boundary condition specifies the normal derivative of potential along the boundary.
Robin. The Robin boundary condition is sort of a mix between Dirichlet and Neumann, prescribing a
relationship between the value of A and its normal derivative at the boundary.
Periodic.A periodic boundary conditions joins two boundaries together. In this type of boundary
condition, the boundary values on corresponding points of the two boundaries are set equal to one
another.
Antiperiodic. The antiperiodic boundary condition also joins together two boundaries. However, the
boundary values are made to be of equal magnitude but opposite sign.)
-
3.1.7 Define circuits.
Select menu PropertiesCircuits. Add a circuit named I with type Series. The value of circuit can be defined as we need. Here we set it to 60A just to make an example.
Figure 3-6 Circuit Property
3.1.8 Place Block Labels
Put one label on each block as shown below.
Figure 3-7 Labels
3.1.9 Associate Properties with Block Labels
Right click on the inner label under function Operate on the block label. Set it to air.
Then select the label on coil. Call the dialogue box, set block type to 16AWG, in circuit
I, number of turns to 50, denoting that the region is filled with 50 turns wrapped in a
counter-clockwise direction. And if we want to denote that the turns are wrapped in a
clockwise direction instead, we could change the current to -I. Also, we should uncheck the
box Let triangle choose Mesh Size and make the mesh size to 0.1, which can let the
program draw more meshes.
The last label will be set to Air too.
-
Figure 3-8 Block Type
Figure 3-9 Final model
This is the finished model.
-
3.1.10 Associate Properties with boundaries.
Select all four sides of the outer square. Press Space bar to set them into boundary type
A=0.
Figure 3-10 Boundary Property
3.1.11 Generate Mesh and Run FEA
Now save the file and click on the toolbar button with yellow mesh . If the mesh spacing
seems to fine or too coarse you can select block labels or line segments and adjust the mesh
size defined in the properties of each object.
Figure 3-11 Mesh
-
3.1.12 Analysis result
Run analysis first . Click on the glasses icon to view the analysis results.
Figure 3-12 Result
And we can also choose to show vectors in our result. Click on button . For example, we
want to plot the vector for B field. Scaling factor can affect the scale of arrows.
Figure 3-13 Vector Plot Options
Figure 3-14 Result with vector
-
Click on button . Then in the dialogue box, check the option Show density plot
Figure 3-15 Dialog
Figure 3-16 Result with density plot
Figure 3-17Result with density plot (zoom)
-
3.1.13 Plot Field Values
First, draw a contour from center(0, 3) to the outer boundary (-5, 3).
Figure 3-18 Contour
Then click on button , choose to plot type |B|Magnitude of flux density.
Figure 3-19 |B| plot
Figure 3-20 |H| plot
-
3.2 Air gap
Here we have a square coil with air gap which is built up by 50 turns of wire. The wire is
copper 16 AWG. The length of its side is 6cm and the length of air gap is 0.75cm. Through
the wire flows a current of 60A.
12
Figure 3-21 Coil with air gap
Please draw a plot with magnetic flux density.
3.2.1 Create new file
FileNew Current Flow Problem
3.2.2 Set Problem Definition
Problem Type: Planar
Length Units: Centimeters
Frequency: 0
Depth: 1
Solver Precision
Min Angle: 30
AC Solver: Succ. Approx
Figure 3-22 Problem definition 12http://upload.wikimedia.org/wikipedia/commons/1/13/EisenkernMitLuftspalt.svg
-
3.2.3 Draw boundary
Draw a boundary to be the solution region that we are interested in. The shape and area of
this region can be selected as you want. Here, we draw it as a square, so that we can have a
axisymmetric solution. Point nodes at (-15, -10), (-15, 14), (20, 14), (20, -10), then connect
them to make a square boundary.
3.2.4 Create a new core and coil
Draw a model with air gap the center of boundary to make the core.
Point nodes at (0, 0), (0, 6), (6, 6), (6, 0), (1, 5), (5, 1), (5, 5), (1, 5), (5, 3.5), (6, 3.5), (5, 2.75),
(6, 2.75).
Point nodes at (-0.25, 4.5), (-0.25, 1.5), (0, 4.5), (0, 1.5), (1, 4.5), (1, 1.5), (1.25, 4.5), (1.25,
1.5). Then connect them as shown to make the coil.
Figure 3-23 Coil
3.2.5 Add material properties
PropertiesMaterials Library Find the material we need in this library and drag it to the Model Materials box. Here we
need material Air and 16 AWG.
3.2.6 Define boundary
Select PropertiesBoundary from the main menu , then click on the Add Property button. Rename the boundary to A=0and Select type to Prescribed A, which means here
we selected Dirichlet to be the boundary condition. Fill all the values with 0. Then click on
OK.
3.2.7 Define circuits.
Select menu PropertiesCircuits. Add a circuit named I with type Series. The value of circuit can be defined as we need. Here we set it to 60A just to make an example.
-
Figure 3-24 Circuit
3.2.8 Place Block Labels
Put one label on each block as shown below.
Figure 3-25 Labels
3.2.9 Associate Properties with Block Labels
Right click on the inner label under function Operate on the block label. Set it to air.
Then select the label on coil. Call the dialogue box, set block type to Coil, in circuit I,
number of turns to 50, denoting that the region if filled with 50 turns wrapped in a
counter-clockwise direction. Also, we should uncheck the box Let triangle choose Mesh
Size and make the mesh size to 0.2, which can let the program draw more meshes.
Figure 3-26 Block type
-
Figure 3-27 Final model
This is the finished model.
3.2.10 Associate Properties with boundaries.
Select all four sides of the outer square. Press Space bar to set them into boundary type
A=0.
Figure 3-28 Boundary property
3.2.11 Generate Mesh and Run FEA
Now save the file and click on the toolbar button with yellow mesh . If the mesh spacing
seems to fine or too coarse you can select block labels or line segments and adjust the mesh
size defined in the properties of each object.
-
Figure 3-29 Mesh
3.2.12 Analysis result
Run analysis first .Click on the glasses icon to view the analysis results.
Figure 3-30 Result
-
And we can also choose to show vectors in our result. Click on button . For example, we
want to plot the vector for B field. Scaling factor can affect the scale of arrows.
Figure 3-31 Result with vectors
Click on button . Then in the dialogue box, check the option Show density plot
Figure 3-32 Result with density plot
Figure 3-33 Result (zoom)
-
3.2.13 Plot Field Values
Draw contour from (3, 3.1) to (9, 3.1), so it will be across the air gap right in the middle.
Then click on and select |B| plot.
Figure 3-34 Contour
Figure 3-35 |B| plot
Figure 3-36 |H| plot
-
Bibliography
Finite Element Method Magnetics: Version 4.2Users ManualDavid Meeker May 29, 2009
Electrostatics: Theory and Applications by Camille L. Bertrand Physics for Engineers and Scientists by H.C. Ohanian, J.T. Markert (2007). 1 (3rd ed.). Norton. ISBN 9780393930030.
Electromagnetics, by Rothwell and Cloud Electric field in Electricity and Magnetism, R Nave http://upload.wikimedia.org/wikipedia/commons/b/b8/Cylindrical_CapacitorII.svg
http://upload.wikimedia.org/wikipedia/commons/3/3f/Spherical_Capacitor.svg
http://upload.wikimedia.org/wikipedia/commons/2/20/Plate_CapacitorII.svg
http://img.tfd.com/mgh/cep/thumb/Magnetic-circuit-with-an-air-gap.jpg
-
List of figures
Figure 1-1 Create a new problem dialogue box .......................................................... 10
Figure 1-2 Problem definition dialogue box ............................................................... 10
Figure 1-3 New model ................................................................................................. 11
Figure 1-4 Linear property .......................................................................................... 11
Figure 1-5 Properties menu ......................................................................................... 12
Figure 1-6Cylinder capacitor ....................................................................................... 12
Figure 1-7 Voltage on layer 1 ...................................................................................... 13
Figure 1-8 Ground ....................................................................................................... 13
Figure 1-9 Layer 1, 2, 3 ............................................................................................... 13
Figure 1-10Property of material 1 ............................................................................... 13
Figure 1-11Property of material 2 ............................................................................... 14
Figure 1-12 Properties for selected block dialogue box .............................................. 14
Figure 1-13 Final model .............................................................................................. 14
Figure 1-14 Mesh ........................................................................................................ 15
Figure 1-15 Result ....................................................................................................... 15
Figure 1-16 X-Y plot of field Values dialogue box..................................................... 16
Figure 1-17 Contour .................................................................................................... 16
Figure 1-18E,t plot ....................................................................................................... 17
Figure 1-19 Change number of points in plot ............................................................. 17
Figure 1-20E,t plot with 600 points in it ..................................................................... 17
Figure 1-21 Point Props ............................................................................................... 18
Figure 1-22 Point info ................................................................................................. 18
Figure 1-23 Problem definition dialogue box ............................................................. 19
Figure 1-24 New model step 1 .................................................................................... 19
Figure 1-25 New model step 2 .................................................................................... 20
Figure 1-26 Properties menu ....................................................................................... 20
Figure 1-27 Cylinder capacitor .................................................................................... 20
Figure 1-28 Voltage on layer 1 .................................................................................... 21
Figure 1-29 Ground ..................................................................................................... 21
Figure 1-30 Layer 1 None Gnd
............................................................................................................................. 22
Figure 1-31Property of material 1 ............................................................................... 22
Figure 1-32Property of material 2 ............................................................................... 22
Figure 1-33Property of material 3 ............................................................................... 22
Figure 1-34 Properties for selected block dialogue box .............................................. 23
Figure 1-35 Mesh ........................................................................................................ 23
Figure 1-36 Result ....................................................................................................... 24
Figure 1-37 Result (zoom) ........................................................................................... 24
Figure 1-38 Contour .................................................................................................... 25
Figure 1-39 E,t plot ...................................................................................................... 25
Figure 1-40 Voltages on two points U1 and U2 ....................................................... 25
Figure 1-41 Ue8-1 ....................................................................................................... 26
Figure 1-42 Problem definition dialogue box ............................................................. 26
-
Figure 1-43 Nodes ....................................................................................................... 27
Figure 1-44 Enter point dialogue box .......................................................................... 27
Figure 1-45 Copy dialogue box ................................................................................... 28
Figure 1-46 x-axis ........................................................................................................ 28
Figure 1-47 Final model .............................................................................................. 28
Figure 1-48 Property of material ................................................................................. 29
Figure 1-49 Conductor 1 ............................................................................................. 29
Figure 1-50 Total voltage ............................................................................................ 29
Figure 1-51 Conductor 2 ............................................................................................. 30
Figure 1-52 Ground ..................................................................................................... 30
Figure 1-53 Result ....................................................................................................... 31
Figure 1-54 Result (zoom) ........................................................................................... 31
Figure 1-55E,t plot ....................................................................................................... 31
Figure 1-56 Info on each layer .................................................................................... 32
Figure 1-57 Ue8-2 ....................................................................................................... 32
Figure 1-58 Capacitor .................................................................................................. 33
Figure 1-59Model Cross section.................................................................................. 34
Figure 1-60Cylinder capacitor ..................................................................................... 34
Figure 1-61 Material properties ................................................................................... 34
Figure 1-62 Conductor properties ............................................................................... 35
Figure 1-63 Conductor attachments ............................................................................ 35
Figure 1-64 Final model .............................................................................................. 35
Figure 1-65 Mesh ........................................................................................................ 36
Figure 1-66Result ........................................................................................................ 36
Figure 1-67Contour ..................................................................................................... 37
Figure 1-68E,t plot ....................................................................................................... 37
Figure 1-69 Info on each layer .................................................................................... 38
Figure 1-70 Hollow sphere .......................................................................................... 38
Figure 1-71 Problem Definition .................................................................................. 39
Figure 1-72 New model ............................................................................................... 39
Figure 1-73 Node in center of circle ............................................................................ 39
Figure 1-74 Nodal property dialogue box ................................................................... 40
Figure 1-75Sphere Capacitor ....................................................................................... 40
Figure 1-76Material property ...................................................................................... 40
Figure 1-77Attach conductors to their properties ........................................................ 41
Figure 1-78Attach node to its property........................................................................ 41
Figure 1-79 .................................................................................................................. 41
Figure 1-80 Result ....................................................................................................... 42
Figure 1-81 Contour .................................................................................................... 42
Figure 1-82E,t plot ....................................................................................................... 42
Figure 1-83D,t plot ...................................................................................................... 43
Figure 1-84 Mesh ........................................................................................................ 43
Figure 1-85 Uncheck the box ...................................................................................... 44
Figure 1-86 New meshes ............................................................................................. 44
Figure 1-87 New result ................................................................................................ 44
Figure 1-88 New zoom ................................................................................................ 45
-
Figure 1-89 New model ............................................................................................... 45
Figure 1-90 Circle in the center ................................................................................... 46
Figure 1-91 Sphere capacitor ....................................................................................... 46
Figure 1-92 Properties of material ............................................................................... 46
Figure 1-93 Properties of conductor ............................................................................ 46
Figure 1-94 Attach conductor to its property (part 1) ................................................. 47
Figure 1-95 Attach conductor to its property (part 2) ................................................. 47
Figure 1-96 Mesh ........................................................................................................ 48
Figure 1-97 Mesh (zoom) ............................................................................................ 48
Figure 1-98 Result ....................................................................................................... 48
Figure 1-99 Contour .................................................................................................... 49
Figure 1-100 X-Y plot of field values dialogue box ................................................... 49
Figure 1-101E,t plot ..................................................................................................... 49
Figure 1-102D,t plot .................................................................................................... 50
Figure 1-103 Problem Definition ................................................................................ 50
Figure 1-104 New model ............................................................................................. 51
Figure 1-105 Properties of material 2 .......................................................................... 51
Figure 1-106 Properties of material 2 .......................................................................... 51
Figure 1-107 Plate capacitor ........................................................................................ 51
Figure 1-108 Properties of conductor .......................................................................... 52
Figure 1-109Attach conductors to their properties ...................................................... 52
Figure 1-110 Mesh ...................................................................................................... 52
Figure 1-111Result ...................................................................................................... 53
Figure 1-112Contour ................................................................................................... 53
Figure 1-113 X-Y plot of field values dialogue box ................................................... 53
Figure 1-114E,t plot ..................................................................................................... 54
Figure 1-115 Voltages ................................................................................................. 54
Figure 1-116 Detail info .............................................................................................. 54
Figure 2-1 New model ................................................................................................. 56
Figure 2-2 Property of material 1 ................................................................................ 56
Figure 2-3 Property of material 2 ................................................................................ 56
Figure 2-4 Voltage on layer 1 ...................................................................................... 57
Figure 2-5Voltage on layer 3 ....................................................................................... 57
Figure 2-6 Final model ................................................................................................ 58
Figure 2-7 Mesh .......................................................................................................... 58
Figure 2-8 Result ......................................................................................................... 58
Figure 2-9 Contour ...................................................................................................... 59
Figure 2-10|E| plot ....................................................................................................... 59
Figure 2-11E,t plot ....................................................................................................... 59
Figure 2-12New model step 1 ..................................................................................... 60
Figure 2-13 New model step 2 .................................................................................... 61
Figure 2-14 Voltage on layer 1 .................................................................................... 61
Figure 2-15 Gnd .......................................................................................................... 61
Figure 2-16 Attach conductor to its property .............................................................. 62
Figure 2-17 Layer 1 Gnd ...... 62
Figure 2-18 Property of material 1 .............................................................................. 62
-
Figure 2-19Property of material 2 ............................................................................... 63
Figure 2-20 Final model .............................................................................................. 63
Figure 2-21 Mesh ........................................................................................................ 64
Figure 2-22 Result ....................................................................................................... 64
Figure 2-23 Result (zoom) ........................................................................................... 64
Figure 2-24 Contour .................................................................................................... 65
Figure 2-25E,t plot ....................................................................................................... 65
Figure 2-26 |E| plot ...................................................................................................... 65
Figure 3-1 Coil wrapped up with copper wire ............................................................. 66
Figure 3-2 Problem definition ..................................................................................... 67
Figure 3-3 Core ............................................................................................................ 67
Figure 3-4 Coil ............................................................................................................ 67
Figure 3-5 Material Library ......................................................................................... 68
Figure 3-6 Circuit Property ......................................................................................... 69
Figure 3-7 Labels ......................................................................................................... 69
Figure 3-8 Block Type ................................................................................................. 70
Figure 3-9 Final model ................................................................................................ 70
Figure 3-10 Boundary Property ................................................................................... 71
Figure 3-11 Mesh ........................................................................................................ 71
Figure 3-12 Result ....................................................................................................... 72
Figure 3-13 Vector Plot Options ................................................................................. 72
Figure 3-14 Re